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Simplifying x2 + x + -343 = 0 Reorder the terms: -343 + x + x2 = 0 Solving -343 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '343' to each side of the equation. -343 + x + 343 + x2 = 0 + 343 Reorder the terms: -343 + 343 + x + x2 = 0 + 343 Combine like terms: -343 + 343 = 0 0 + x + x2 = 0 + 343 x + x2 = 0 + 343 Combine like terms: 0 + 343 = 343 x + x2 = 343 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 343 + 0.25 Reorder the terms: 0.25 + x + x2 = 343 + 0.25 Combine like terms: 343 + 0.25 = 343.25 0.25 + x + x2 = 343.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 343.25 Calculate the square root of the right side: 18.527007314 Break this problem into two subproblems by setting (x + 0.5) equal to 18.527007314 and -18.527007314.Subproblem 1
x + 0.5 = 18.527007314 Simplifying x + 0.5 = 18.527007314 Reorder the terms: 0.5 + x = 18.527007314 Solving 0.5 + x = 18.527007314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 18.527007314 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 18.527007314 + -0.5 x = 18.527007314 + -0.5 Combine like terms: 18.527007314 + -0.5 = 18.027007314 x = 18.027007314 Simplifying x = 18.027007314Subproblem 2
x + 0.5 = -18.527007314 Simplifying x + 0.5 = -18.527007314 Reorder the terms: 0.5 + x = -18.527007314 Solving 0.5 + x = -18.527007314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -18.527007314 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -18.527007314 + -0.5 x = -18.527007314 + -0.5 Combine like terms: -18.527007314 + -0.5 = -19.027007314 x = -19.027007314 Simplifying x = -19.027007314Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.027007314, -19.027007314}
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